On the number of generators of a projective module

In this article we give a bound on the number of generators of a finitely generated projective module of constant rank over a commutative Noetherian ring in terms of the rank of the module and the dimension of the ring. Under certain conditions we provide an improvement to the Forster–Swan bound in case of finitely generated projective modules of rank n over an affine algebra over a finite field or an algebraically closed field.